How do you find the inverse of f(x)=(6x+4)/(4x+5) and graph both f and f^-1?

Mar 4, 2017

The inverse is ${f}^{-} 1 \left(x\right) = \frac{4 - 5 x}{4 x - 6}$

Explanation:

We have

$f \left(x\right) = \frac{6 x + 4}{4 x + 5}$

Let $y = \frac{6 x + 4}{4 x + 5}$

Therefore,

$y \left(4 x + 5\right) = 6 x + 4$

$4 x y + 5 y = 6 x + 4$

$4 x y - 6 x = 4 - 5 y$

$x \left(4 y - 6\right) = \left(4 - 5 y\right)$

$x = \frac{4 - 5 y}{4 y - 6}$

So,

The inverse of $f \left(x\right)$ is

${f}^{-} 1 \left(x\right) = \frac{4 - 5 x}{4 x - 6}$

graph{(y-(6x+4)/(4x+5))(y-(4-5x)/(4x-6))(y-x)=0 [-8.89, 8.89, -4.44, 4.45]}